Sin Cos Tan Calculator

Sine, Cosine, Tangent Calculator

function calculateTrigFunctions() { var angleInput = document.getElementById('angleInput').value; var unitSelect = document.getElementById('unitSelect').value; var angle = parseFloat(angleInput); if (isNaN(angle)) { document.getElementById('sinResult').innerText = 'Please enter a valid number.'; document.getElementById('cosResult').innerText = "; document.getElementById('tanResult').innerText = "; return; } var angleInRadians; if (unitSelect === 'degrees') { angleInRadians = angle * (Math.PI / 180); } else { angleInRadians = angle; } var sinValue = Math.sin(angleInRadians); var cosValue = Math.cos(angleInRadians); var tanValue = Math.tan(angleInRadians); document.getElementById('sinResult').innerText = sinValue.toFixed(6); document.getElementById('cosResult').innerText = cosValue.toFixed(6); // Handle tangent for angles where it's undefined (e.g., 90, 270 degrees) if (unitSelect === 'degrees' && (Math.abs(angle % 180) === 90)) { document.getElementById('tanResult').innerText = 'Undefined'; } else if (Math.abs(cosValue) < 1e-9) { // Check if cosine is very close to zero for radians document.getElementById('tanResult').innerText = 'Undefined'; } else { document.getElementById('tanResult').innerText = tanValue.toFixed(6); } }

Understanding Sine, Cosine, and Tangent

Sine, Cosine, and Tangent are fundamental trigonometric functions that describe the relationships between the angles and sides of a right-angled triangle. They are crucial in various fields, including mathematics, physics, engineering, and computer graphics.

What are They?

Consider a right-angled triangle with an angle θ (theta). The sides are defined relative to this angle:

• Opposite: The side directly across from angle θ.
• Adjacent: The side next to angle θ that is not the hypotenuse.
• Hypotenuse: The longest side, opposite the right angle.

The trigonometric functions are defined as ratios of these sides:

• Sine (θ): Ratio of the length of the Opposite side to the length of the Hypotenuse.
  sin(θ) = Opposite / Hypotenuse
• Cosine (θ): Ratio of the length of the Adjacent side to the length of the Hypotenuse.
  cos(θ) = Adjacent / Hypotenuse
• Tangent (θ): Ratio of the length of the Opposite side to the length of the Adjacent side. It can also be expressed as tan(θ) = sin(θ) / cos(θ).
  tan(θ) = Opposite / Adjacent

Degrees vs. Radians

Angles can be measured in two primary units: degrees or radians.

• Degrees: A full circle is 360 degrees. This is the most common unit for everyday use and geometry.
• Radians: A full circle is 2π radians. Radians are often preferred in higher mathematics and physics because they simplify many formulas, especially those involving calculus.

Our calculator allows you to choose between these two units, automatically converting to radians internally for calculation as standard mathematical functions typically operate on radians.

How to Use This Calculator

1. Enter Angle Value: Input the numerical value of the angle you wish to analyze into the "Angle Value" field.
2. Select Angle Unit: Choose whether your angle is in "Degrees" or "Radians" using the dropdown menu.
3. Click Calculate: Press the "Calculate" button to see the sine, cosine, and tangent values for your specified angle.

Examples

Let's look at some common angles and their trigonometric values:

• Angle: 30 Degrees
  • sin(30°) = 0.5
  • cos(30°) &approx; 0.866
  • tan(30°) &approx; 0.577
• Angle: 45 Degrees
  • sin(45°) &approx; 0.707
  • cos(45°) &approx; 0.707
  • tan(45°) = 1
• Angle: 90 Degrees
  • sin(90°) = 1
  • cos(90°) = 0
  • tan(90°) = Undefined (as cos(90°) is 0, leading to division by zero)
• Angle: π/2 Radians (equivalent to 90 degrees)
  • sin(π/2) = 1
  • cos(π/2) = 0
  • tan(π/2) = Undefined

This calculator provides a quick and accurate way to find these values, aiding in your mathematical and scientific endeavors.